This course presents the student with advanced techniques for analysing the behaviour of solutions of ordinary differential equations. Topics include systems of first order linear differential equations, existence and uniqueness of solutions; adjoint systems,  linear system associated with a linear homogeneous differential equation of order n,  adjoint equation to a linear homogeneous differential equation, Lagrange Identity, linear boundary value problems on a finite interval; homogeneous boundary value problems and Green’s function; non-self-adjoint boundary value problems, self-adjoint eigenvalue problems on a finite interval, the expansion and completeness theorems, oscillation and comparison theorem for second-order linear equations and applications.